We study clones on a four-element set related to the clone $${\mathsf {DMA}}$$ of all term functions subdirectly irreducible De Morgan algebra $${\mathbf {DM}}_{{{\mathbf {4}}}}$$ . find generating sets for preserving subalgebras , automorphisms truth order and information as well defined by conjunctions these conditions. identify covers in lattice four-valued describe above which contain discr...

The paper considers the fundamental notions of manyvalued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite v...

A great deal of recent theoretical work in inference has involved extending classical logic in some way. I argue that these extensions share two properties: firstly, the formal addition of truth values encoding intermediate levels of validity between true (i.e., valid) and false (i.e., invalid) and, secondly, the addition of truth values encoding intermediate levels of certainty between true or...

Many-valued models, besides providing a natural semantical interpretation for several non-classical logics, constitute a very sharp tool for investigating and understanding meta-logical properties in general. Although open to debates from the philosophical perspective, seen from the mathematical viewpoint many-valued matrices and algebras are perfectly well-defined mathematical objects with sev...

In earlier work [9], we defined CTL model-checking over finite-valued logics with De Morgan negation. In this paper, we extend this work to logics with intuitionistic, Galois and minimal negations, calling the resulting language CTL. We define CTL operators and show that they can be computed using fixpoints. We further discuss how to extend our existing multi-valued model-checker Chek [8] to re...

In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between...